Dynamics of contentment

TL;DR

This paper introduces a dynamic model linking individual wealth and contentment, deriving equations for their joint evolution, and demonstrates how wealth taxation impacts societal wealth and satisfaction over time.

Contribution

It develops a novel mathematical framework for the joint evolution of wealth and contentment, incorporating the effects of taxation on societal distribution.

Findings

Higher wealth taxes can lead to a wealthier and more content society over time.

Lower tax rates may cause societal stratification in wealth and contentment.

No direct correlation between average wealth and contentment levels.

Abstract

A continuous variable changing between 0 and 1 is introduced to characterise contentment, or satisfaction with life, of an individual and an equation governing its evolution is postulated from analysis of several factors likely to affect the contentment. As contentment is strongly affected by material well-being, a similar equation is formulated for wealth of an individual and from these two equations derived an evolution equation for the joint distribution of individuals' wealth and contentment within a society. The equation so obtained is used to compute evolution of this joint distribution in a society with initially low variation of wealth and contentment over a long period time. As illustration of this model capabilities, effects of the wealth tax rate are simulated and it is shown that a higher taxation in the longer run may lead to a wealthier and more content society. It is also shown that lower rates of the wealth tax lead to pronounced stratification of the society in terms of both wealth and contentment and that there is no direct relationship between the average values of these two variables.